Weak Coupling Chambers in N=2 BPS Quiver Theory

In this thesis we review the Seiberg-Witten solution of four dimensional N=2 gauge theories, the six-dimensional construction of these models recently proposed by Gaiotto and the BPS quiver technique for the determination of the BPS spectrum of N=2 theories. We then study how these recent developments allow to better understand nonperturbative aspects such as confinement and dynamical symmetry breaking in the N=1 theories obtained starting from N=2 SQCD and adding a mass term...

We consider a general class of symmetries of hyper-Kahler quotients which can be interpreted as classical analogs of Seiberg duality for N=2 supersymmetric quiver gauge theories in the baryonic Higgs branch. Along the way we find that a limit application of this duality yields new exotic realizations of ALE spaces as hyper-Kahler quotients. We also discuss how these results admit in some particular cases a natural interpretation in string theory. We finally comment on a possi...

We propose a universal manipulation to obtain Seiberg-like dualities of 3d $\mathcal{N}=2$ general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter fields. We illustrate this with several examples of linear, circular and star-shaped quiver gauge theories. We examine the local operators in the theories by computing supersymmetric indices and also find precise matching for the proposed dualities as strong...

We argue how to identify supersymmetric quiver quantum mechanics description of BPS states, which arise in string theory in brane systems representing knots. This leads to a surprising relation between knots and quivers: to a given knot we associate a quiver, so that various types of knot invariants are expressed in terms of characteristics of a moduli space of representations of the corresponding quiver. This statement can be regarded as a novel type of categorification of k...

We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which can be treated with semiclassical methods in the weak coupling limit, is the decay of quark-soliton bound states. For a quark and a soliton of electric-magnetic charge vectors $Q$ and $Q^\prime$ respectively, we find that as the manifold o...

We present a detailed study of the analytic structure, BPS spectra and superconformal points of the $ N=2 $ susy $ SU(2) $ gauge theories with $ N_f=1,2,3 $ massive quark hypermultiplets. We compute the curves of marginal stability with the help of the explicit solutions for the low energy effective actions in terms of standard elliptic functions. We show that only a few of these curves are relevant. As a generic example, the case of $ N_f=2 $ with two equal bare masses is st...

We study the BPS spectrum in $D=4, N=4$ heterotic string compactifications, with some emphasis on intermediate $N=4$ BPS states. These intermediate states, which can become short in $N=2$ compactifications, are crucial for establishing an $S-T$ exchange symmetry in $N=2$ compactifications. We discuss the implications of a possible $S-T$ exchange symmetry for the $N=2$ BPS spectrum. Then we present the exact result for the 1-loop corrections to gravitational couplings in one o...

Supersymmetric Sp(k) quantum chromodynamics with 8 supercharges in space-time dimensions 3 to 6 can be realised by two different Type II brane configurations in the presence of orientifolds. Consequently, two types of magnetic quivers describe the Higgs branch of the Sp(k) SQCD theory. This is a salient example of a general phenomenon: a given hyper-Kahler Higgs branch may admit several magnetic quiver constructions. It is then natural to wonder if these different magnetic qu...

We define the notion of a complete N=2 supersymmetric theory in 4 dimensions as a UV complete theory for which all the BPS central charges can be arbitrarily varied as we vary its Coulomb branch parameters, masses, and coupling constants. We classify all such theories whose BPS spectrum can be obtained via a quiver diagram. This is done using the 4d/2d correspondence and by showing that such complete N=2 theories map to quivers of finite mutation type. The list of such theori...

We discuss a general procedure to obtain 1/2 BPS partition functions for generic N=1 quiver gauge theories. These functions count the gauge invariant operators (bosonic and fermionic), charged under all the global symmetries (mesonic and baryonic), in the chiral ring of a given quiver gauge theory. In particular we discuss the inclusion of the spinor degrees of freedom in the partition functions.